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For example in this link you can see a 2 speed gearbox for a high speed boat http://www.coanracing.com/custom-block2/transmissions.html/xtreme-marine-transmission.html , what even is the purpose of having different speeds in a boat? In the link it says it allows faster accleration and better manuevering at low speeds but how exactly does a transmission help with those things in a boat or a ship and why dont other ships also use them? This just seems like its only used by high speed boats but i might be wrong.

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It's for exactly the same reason that cars have multispeed transmissions, as follows.

Power is always the product of torque times RPM (times the right conversion constants to account for units). This means an internal combustion engine produces peak power when it is running at the highest RPM it can handle without blowing up.

But when initially accelerating from zero velocity, the engine cannot spin its propeller at full speed because its propeller is pitched to match the load presented to the engine when the boat is travelling at its maximum speed. By putting a reduction gear into the driveline, the engine can then spin all the way up to its redline, at which point it is screaming its guts out- and delivering its maximum power output to the prop and hence developing maximum acceleration for the boat.

This extra oomph sets the boat in motion as quickly as possible- after which you clutch out the reduction gear, slam it into direct drive and max the throttle until you hit redline again.

Note that it is common for boat owners to use one prop for yanking water skiers up and out of the water as quickly as possible, and a second prop for maximum top speed. The pull prop often has four blades for maximum thrust and the speed prop will have just two. A compromise prop will have three blades. So on water ski day, the pull prop is installed and on race day, the speed prop is installed.

This process is done in racing cars and motorcycles with as many as 6 or 7 different drive ratios, to keep the engine running up at its max power point no matter what the wheel speed is.

In airplanes, this same thing is done by changing the blade pitch instead of shifting gears. You set fine pitch for takeoff to spin the engine up to max power and as your speed builds, you dial in more bite to the blades. In inexpensive planes (just like in boats), you instead choose between installing one of two different propellers: the fine-pitch model is called a climb prop and the deep-pitch model is called a cruise prop.

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